46 OUT1NES OF NATURAL PHILOSOPHY. 



The radius of curvature at the parallel of 45, or 

 m D, is nearly an arithmetical mean between the 

 radius of the equator and half the earth's axis. 



The degree in the parallel of 4? 5 is also an arithmeti- 

 cal mean between any two degrees equally distant 

 from it on the north and on the south. 



c. The degree in any latitude is understood to be that 

 of which the middle point is in that latitude. 



f. If, therefore, D be found by actual measurement in 

 any two known latitudes, we shall have two equa- 

 tions, in which a and c are the only unknown 

 quantities, and from which, therefore, they may be 

 determined. 



59. The lengths of two degrees, of which the 

 middle points are in given latitudes, being 

 known ; it is required from thence to determine 

 the diameter of the equator, and the axis of the 

 earth, that is, the longer and the shorter axis of 

 the elliptic meridian. 



a. Let D and D' be the given degrees, (the least, or that 

 nearest the equator, being D), A and >f the lati- 

 tudes of their middle points, a the semitransverse 

 axis of the meridian, c the difference of the semi- 

 axis ; we have the equations, 



ml) == 



